Question

Дан прямоугольник. Его ширина равна x см, а длина в 4 раза больше ширины. Выбери формулу, описывающую зависимость площади данного прямоугольника от его ширины. Ответь на вопрос, является ли данная зависимость линейной функцией? Помогите срочно(((2

Answer 1

Ответ:

Объяснение:

 Нехай ширина пр - ка  b = x cм ; тоді його довжина  a = 4x cм .

     S = a * b = 4x * x = 4x² ; S( x ) = 4x² - залежність площі  пр - ка

 від його ширини . Дана залежність не є лінійною функцією , бо

  вона не має  вид   y = kx + b .  

Answer 2

Formula for the Area of a Rectangle

To find the formula that describes the relationship between the width and area of a rectangle, we need to consider the given information.

Let's denote the width of the rectangle as x cm. According to the problem, the length of the rectangle is 4 times the width. Therefore, the length can be expressed as 4x cm.

The formula for the area of a rectangle is given by multiplying the width and length:

Area = width * length

Substituting the values we have:

Area = x * 4x

Simplifying the expression:

Area = 4x^2

Therefore, the formula that describes the relationship between the width and area of the given rectangle is Area = 4x^2.

Linearity of the Relationship

To determine if the relationship between the width and area of the rectangle is linear, we need to check if the formula satisfies the properties of a linear function.

A linear function is defined as a function that can be represented by a straight line. It has the general form y = mx + b, where m is the slope of the line and b is the y-intercept.

In the formula we derived for the area of the rectangle (Area = 4x^2), we can see that the exponent of x is 2. This indicates that the relationship is quadratic, not linear.

Therefore, the relationship between the width and area of the given rectangle is not a linear function.

I hope this explanation helps! Let me know if you have any further questions.